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Conference on Non-integer Order Calculus and Its Applications

RRNR 2018: Advances in Non-Integer Order Calculus and Its Applications pp 72–85Cite as

Numerical Simulations for Fitting Parameters of Linear and Logistic-Type Fractional-, Variable-Order Equations - Comparision of Methods

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

Abstract

In the work variable-, fractional-order backward difference of the Grünwald-Letnikov type is presented. The backward difference is used to generate simulated experimental data to which additional noise signal is added. Using prepared data four different algorithms of finding the parameter of the order function (assuming that the general family of the function is known) and constant \(\lambda \) coefficient are compared. The algorithms are: trust region algorithm, particle swarm algorithm, simulated annealing algorithm and genetic algorithm.

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References

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Acknowledgment

The work was supported by Polish founds of National Science Center, granted on the basis of decision DEC-2016/23/B/ST7/03686.

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Authors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351, Białystok, Poland

    Piotr Oziablo

Authors
  1. Piotr Oziablo
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Correspondence to Piotr Oziablo .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Oziablo, P. (2020). Numerical Simulations for Fitting Parameters of Linear and Logistic-Type Fractional-, Variable-Order Equations - Comparision of Methods. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_6

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